How about 1) Prove for a 4-node, or tetrahedral graph. 2) Demonstrate that all graphs with > 4 nodes are composed of multiple overlapping tetrahedrons 3) Figure out how coupled tetrahedra function when nodes are deleted. 4) Induct on number of tetrahedra in graph. ?

Obviously (3) is the tough part, but why should it be impossible?

## A strategy for simple graphs?

How about 1) Prove for a 4-node, or tetrahedral graph. 2) Demonstrate that all graphs with > 4 nodes are composed of multiple overlapping tetrahedrons 3) Figure out how coupled tetrahedra function when nodes are deleted. 4) Induct on number of tetrahedra in graph. ?

Obviously (3) is the tough part, but why should it be impossible?